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Theorem ax6o 1750
 Description: Show that the original axiom ax-6o 2137 can be derived from ax-6 1729 and others. See ax6 2147 for the rederivation of ax-6 1729 from ax-6o 2137. Normally, ax6o 1750 should be used rather than ax-6o 2137, except by theorems specifically studying the latter's properties. (Contributed by NM, 21-May-2008.)
Assertion
Ref Expression
ax6o x ¬ xφφ)

Proof of Theorem ax6o
StepHypRef Expression
1 sp 1747 . 2 (xφφ)
2 ax-6 1729 . 2 xφx ¬ xφ)
31, 2nsyl4 134 1 x ¬ xφφ)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1540 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-ex 1542 This theorem is referenced by:  a6e  1751  modal-b  1752  hbnt  1775  nfndOLD  1792  equsalhwOLD  1839  ax9o  1950
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